Any intervention in a system or process entails the possibility of gain or loss. For example, a company's new advertising campaign may increase, decrease, or have no effect on sales. As another example, a medical therapy may be effective, ineffective, or detrimental in treating a disease. To evaluate the efficacy of possible intervening “treatments,” a scientist, analyst, marketer, or other investigator may apply the principles of statistical design of experiments. In particular, they may test alternative treatment modalities (often including a control or untreated modality) in two or more randomized groups. In some cases, the treatments may have a definite positive outcome (e.g., increased sales, cured disease, etc.). In such cases, different treatments are often evaluated by comparing the percentage of positive responses in each group, with the difference between the observed rates of response becoming the major determinant of which potential intervention will put into service. In other cases, the outcome of interest may be numerical in nature, such as the total dollars spent by a customer or the systolic blood pressure of a patient. In these “continuous” cases, the difference between the mean (average) values for the alternative treatment modalities is the usual measure of causal effect.
Traditional methods, therefore, produce an “average” estimate of causal effect presumed to be globally applicable. These methods are of very limited use in dealing with individual variability of the causal effect. They effectively assume that the causal effect is uniform across different individuals or, if it varies, that we are interested only in the average effect. If, instead, a researcher wishes to determine the causal effect for a single individual, then these traditional methods may prove ineffective.
One problem, recognized by the present inventors, in estimating a personalized treatment effect is that we can only observe each individual under a single treatment modality. For example, if a first medical treatment cures a person's disease, then there would be no reasonable way to test whether a second treatment would cure the person's disease. As another example, when a person is shown a first advertisement, the person may form such a lasting opinion about the subject of the advertisement that this opinion would alter the efficacy of any future advertisement. More generally, once a person receives a first treatment, they may not react to a second treatment in the same way as a person who initially receives the second treatment.
For every person, therefore, the outcome of only one treatment will ever be observed; while the other outcome (termed a “counterfactual” outcome) remains hidden. Statisticians are thus reduced to dealing with comparisons among groups of individuals. This basic conundrum makes the determination of an effect for each individual technically impossible.